Related papers: Extinction and coming down from infinity of CB-pro…
In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
We describe the solution of an optimal stopping problem for a stable L\'evy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains…
We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…
A study is made of the behavior of unstable states in simple models which nevertheless are realistic representations of situations occurring in nature. It is demonstrated that a non-exponential decay pattern will ultimately dominate decay…
We consider two-dimensional L\'evy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that…
Here we present extinction, extirpation and coexistence conditions where / when two communities combine. We consider one specific model where two communities coalesce, and another model where the communities coexist side by side, blending…
In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses, such as those introduced by a realistic quantum communication channel, e.g. by propagation in an optical fiber. We find that…
We propose and study {a generalized Beverton-Holt competition model} subject to Allee effects to obtain insights on how the interplay of Allee effects and contest competition affects the persistence and the extinction of two competing…
In this paper we consider the diffusive competition model with free boundary in the heterogeneous time-periodic environment, in which the variable intrinsic growth rates of invasive and native species may change signs and be "very negative"…
A competition process on $\mathbb{Z}^d$ is considered, where two species compete to color the sites. The entities are driven by branching random walks. Specifically red (blue) particles reproduce in discrete time and place offspring…
Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The dynamics of this selection is studied using a simple linear model. It has similarities to…
Persistent economic competition is often justified as a mechanism of innovation, efficiency, and welfare maximization. Yet empirical evidence across disciplines reveals that competition systematically generates fragility, inequality, and…
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow 0}|X_t|/t^{\kappa}$, $\limsup_{t\downarrow…
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…